Deep mining has been paid much more attention because of the depletion of shallow mining resources.Traditional bolts could be invalid to accommodate large displacement and deformation in geomaterials.Consequently, alternative support and reinforcement bolts need to be studied and their constitutive models also need to be developed to help understanding for the complex stress-strain responses of rock masses under loadings. The effect of Negative Poisson’s Ratio(NPR) that is attributed to the swelling phenomenon along the lateral direction may appear in metal materials under tensional loadings. Thence NPR materials often have an advantage over NPR ones in mechanical behavior such as impact resistance, antishearing, and energy absorbed. From the characteristics of NPR materials, a series of bolt and cable supports with the effect of NPR and constant-resistance have been recently developed. We here firstly introduce the structural features of NPR support. Then the constitutive model of NPR support is presented and its corresponding equation of energy equilibrium. Its basic principle interacted on rock masses is further discussed. Finally, NPR cables are employed to support the slope of an open-pit mine. The applications show that NPR cables can ease failure within the slope and play an important role in predicting and providing early warning of slope failure, together with a monitoring system of slope stability. Deep mining has been paid much more attention because of the depletion of shallow mining resources .Traditional bolts could be invalid to accommodate large displacement and deformation in geomaterials.Consequently, alternative support and reinforcement bolts need to be studied and their constitutive models also need to be developed to help understanding for the complex stress-strain responses of rock masses under loadings. The effect of Negative Poisson’s Ratio (NPR) that is attributed to the swelling phenomenon along the lateral direction may appear in metal materials under tensional loadings. Thence NPR materials often have an advantage over NPR ones in mechanical behavior such as impact resistance, antishearing, and energy absorbed. From the characteristics of NPR materials, a series of bolt and cable supports with the effect of NPR and constant-resistance have been recently developed. then introduce the structural features of NPR support. Then the constitutive model of NPR Its basic principle interacted on rock masses is further discussed. Finally, NPR cables are employed to support the slope of an open-pit mine. The applications show that NPR cables can ease failure within the slope and play an important role in predicting and providing early warning of slope failure, together with a monitoring system of slope stability.